Variable direction tooth attachments

ABSTRACT

Tooth attachments are provided comprising one or more convex surfaces for engagement by a surface of an orthodontic appliance. Polymeric shell appliances are provided in which the polymeric shell appliances are configured to provide one or more activation forces to facilitate tooth movement. The polymeric shell appliances may comprise one or more tooth receiving cavities. The polymeric shell appliances may further comprise an engagement portion with a surface configured to engage a convex attachment surface in order to apply a tooth moving force.

CROSS-REFERENCE

This application is a divisional application of U.S. application Ser.No. 15/046,193, filed Feb. 17, 2016, now U.S. Pat. No. 10,045,835,issued Aug. 14, 2018, which is incorporated herein by reference in itsentirety and to which application we claim priority under 35 USC § 120.

BACKGROUND

Prior methods and apparatus for moving teeth can be less than ideal inat least some respects. Although orthodontic shell appliances can beeffective in moving teeth, complex tooth movements may be benefit fromthe use of attachments on the teeth that engage the appliance to movethe tooth. Although attachments can be effective, complex toothmovements may require multiple attachments on the teeth, which can besomewhat cumbersome and unsightly for the patient, as well as difficultfor the orthodontic practitioner to apply. Furthermore, priorattachments can be sensitive to manufacturing variations resulting inunpredictable or inconsistent forces applied to teeth. It would behelpful to provide more versatile and reliable attachments, allowing theorthodontic shell appliances to move teeth more precisely and with lessneed to replace attachments during treatment.

SUMMARY

Embodiments of the present disclosure provide improved systems, methods,and apparatus for moving teeth. In many embodiments, the orthodonticsystems herein include an attachment device having a convex surface. Theconvex surface can engage with an appliance shell to apply repositioningforces to teeth with improved reliability and reduced sensitivity tovariations in manufacturing tolerances. The convex surface of theattachment further allows the application of a plurality of tooth movingforces by contacting the attachment surface at different locations withengagement surfaces of one or more appliances, sequentially and/orconcurrently. In many embodiments, the direction of the tooth movingforces applied may be independently and continuously varied bycontinuously varying the contact location of an engagement portion of anappliance with the convex surface of the attachment. The tooth movingforces applicable by attachments as disclosed herein can be used to moveteeth along any of a wide array of trajectories.

In one aspect, an orthodontic system for repositioning a patient's teethis provided. The system comprises an attachment device configured to becoupled to a tooth of the patient and comprising a convex surface. Thesystem also comprises a plurality of appliance shells each shaped toreceive the patient's teeth, each appliance comprising an engagementportion positioned to engage the convex surface of the attachment deviceso as to apply a repositioning force to the tooth. The engagementportions of at least some of the plurality of appliance shells may eachbe arranged to contact the convex surface at a different respectivelocation so as to apply different respective repositioning forces to thetooth.

In another aspect, a computer-implemented method for processing toothmovement data in order to design an orthodontic system for repositioninga patient's teeth is provided. The computer system receives toothmovement data indicative of a movement trajectory for a tooth of thepatient, and processes data including the tooth movement data so as todetermine a geometry for an attachment device to be coupled to thetooth, the attachment device comprising a convex surface. The computersystem further processes data including the tooth movement data so as todetermine geometries for a plurality of appliance shells, each shaped toreceive the patient's teeth. The plurality of appliance shells for whichthe geometries are determined each comprise an engagement portionpositioned to engage the convex surface of the attachment device so asto apply a repositioning force to the tooth. Optionally, the engagementportions of at least some of the plurality of appliance shells are eacharranged to contact the convex surface at a different respectivelocation so as to apply different respective repositioning forces to thetooth in order to move the tooth along the movement trajectory.

In another aspect, an orthodontic appliance for repositioning apatient's teeth is provided. The appliance comprises an attachmentdevice configured to be coupled to a tooth of the patient and comprisinga convex surface, as well as a shell comprising a plurality of cavitiesshaped to receive the patient's teeth. At least one cavity of theplurality of cavities comprises a receptacle shaped to receive theattachment device, and the receptacle comprises a planar surfacepositioned to engage the convex surface of the attachment device so asto apply a repositioning force to the tooth.

Other objects and features of the present invention will become apparentby a review of the specification, claims, and appended figures.

INCORPORATION BY REFERENCE

All publications, patents, and patent applications mentioned in thisspecification are herein incorporated by reference to the same extent asif each individual publication, patent, or patent application wasspecifically and individually indicated to be incorporated by reference.

BRIEF DESCRIPTION OF THE DRAWINGS

The novel features of the invention are set forth with particularity inthe appended claims. A better understanding of the features andadvantages of the present disclosure will be obtained by reference tothe following detailed description that sets forth illustrativeembodiments, in which the principles of the invention are utilized, andthe accompanying drawings of which:

FIG. 1A illustrates a tooth repositioning appliance, in accordance withmany embodiments;

FIG. 1B illustrates a tooth repositioning system, in accordance withmany embodiments;

FIG. 2 illustrates a method of orthodontic treatment using a pluralityof appliances, in accordance with many embodiments;

FIG. 3 illustrates the interface between an attachment comprising aplanar surface and an engagement portion of an appliance comprising aplanar surface, in accordance with many embodiments;

FIGS. 4A and 4B illustrate how small errors in appliance fabrication canlead to large changes in the location of interaction between a planarappliance surface and a planar attachment surface, in accordance withmany embodiments;

FIG. 5A illustrates an attachment with a convex surface and an applianceconfigured to engage that surface, in accordance with many embodiments;

FIG. 5B illustrates a plurality of appliances, each configured with asurface at a different angle so as to contact a single attachment atdifferent locations, thereby applying different forces, in accordancewith many embodiments;

FIG. 6 illustrates an attachment comprising a convex surface and anon-contacting surface, in addition to an appliance with a surfaceconfigured to engage the convex surface, in accordance with manyembodiments;

FIG. 7A illustrates an attachment with a convex surface and an appliancewith a plurality of surfaces, each configured to concurrently contactthe convex surface at different respective locations so as to apply anet force to a tooth, in accordance with many embodiments;

FIG. 7B illustrates an alternative configuration of the attachment andappliance of FIG. 7A, in which each appliance surface contacts aseparate convex surface of the attachment, in accordance with manyembodiments;

FIG. 7C illustrates an attachment with a convex surface and an appliancewith a plurality of surfaces, each configured to concurrently contactthe convex surface at different respective locations so as to apply anet moment to a tooth, in accordance with many embodiments;

FIGS. 8A-8D illustrate the reduced sensitivity of attachments engaged onconvex surfaces to manufacturing variations, compared to attachmentsengaged on planar surfaces, in accordance with many embodiments;

FIGS. 9A-9E illustrate how a tooth may be moved in a complex trajectorywhile applying forces to a single attachment comprising one or moreconvex engagement surfaces, in accordance with many embodiments;

FIGS. 10A-10E illustrate the use of an attachment comprising one or moreconvex engagement surfaces to rotate a tooth in multiple directions toprovide space to move a second tooth, thereby allowing a complexreorganization of teeth, in accordance with many embodiments;

FIG. 11 illustrates a method of treating a patient using an attachmentcomprising a convex surface and one or more appliances, in accordancewith many embodiments;

FIG. 12 illustrates a method of designing appliances and attachments totreat a patient, in accordance with many embodiments;

FIG. 13 illustrates a method for digitally planning an orthodontictreatment, in accordance with many embodiments; and

FIG. 14 is a simplified block diagram of a data processing system, inaccordance with many embodiments.

DETAILED DESCRIPTION

The present disclosure provides improved systems, methods, and apparatusfor moving a patient's teeth. In many embodiments, the orthodonticsystems herein include an attachment device having a convex surface. Theattachment device is attached to a tooth of a patient. The convexsurface can engage with an appliance shell to apply repositioning forcesto teeth with improved reliability and reduced sensitivity to variationsin manufacturing tolerances. Additionally, the convex surface of theattachment further allows the application of a plurality of tooth movingforces by contacting the attachment surface at different locations withengagement surfaces of one or more appliances, sequentially and/orconcurrently. In many embodiments, the direction of the tooth movingforces applied may be independently and continuously varied bycontinuously varying the contact location of an engagement portion of anappliance with the convex surface of the attachment. This can beadvantageous, since it is often less expensive and difficult to replaceor adjust a removable orthodontic appliance than to replace or adjust anattachment. Applying tooth moving forces using attachments as disclosedherein permits the movement of teeth along various trajectories,including complex trajectories, with greater reliability while allowingchanges in direction without needing to replace the attachment.

As used herein the term “and/or” is used as a functional word toindicate that two words or expressions are to be taken together orindividually. For example, A and/or B encompasses A alone, B alone, andA and B together.

In one aspect, an orthodontic system for repositioning a patient's teethis provided. The system comprises an attachment device configured to becoupled to a tooth of the patient and comprising a convex surface. Thesystem also comprises a plurality of appliance shells each shaped toreceive the patient's teeth, each appliance shell comprising anengagement portion positioned to engage the convex surface of theattachment device so as to apply a repositioning force to the tooth. Inmany embodiments, the engagement portions of at least some of theplurality of appliance shells are each arranged to contact the convexsurface at a different respective location so as to apply differentrespective repositioning forces to the tooth. Optionally, the engagementportions of some or all of the plurality of appliance shells may bearranged to contact the convex surface at the same location, e.g., toreduce susceptibility of appliance performance to manufacturingtolerances.

In many embodiments, the attachment device comprises a single convexsurface.

In many embodiments, the convex surface comprises a spherical,ellipsoidal, or cylindrical shape profile.

In many embodiments, each engagement portion of each appliance shellcomprises a planar surface, and the repositioning force applied by eachengagement portion is oriented along a direction substantially normal tothe planar surface. The amount of friction between the planar surface ofthe engagement portion and the convex surface of the attachment devicemay be relatively low resulting in minimal or no tangential forces. Insome embodiments, the planar surfaces of the at least some of theplurality of appliance shells are each arranged at differentorientations relative to the convex surface.

In many embodiments, the different respective repositioning forcesdiffer from each other with respect to one or more of location ororientation.

In many embodiments, the different respective repositioning forces areconfigured to reposition the tooth along a non-linear movementtrajectory.

In many embodiments, each engagement portion is positioned so as tocontact the convex surface of the attachment device at a singlelocation.

In many embodiments, at least one of the plurality of appliance shellscomprises a plurality of engagement portions positioned to contact theconvex surface at a plurality of different locations.

In many embodiments, the attachment device further comprises anon-contacting surface that does not engage the plurality of applianceshells. The non-contacting surface may be a convex surface or anon-convex surface.

In many embodiments, the system further comprises a second plurality ofappliance shells each shaped to receive the patient's teeth, eachappliance shell of the second plurality of appliance shells comprisingan engagement portion positioned to engage the convex surface of theattachment device so as to apply a repositioning force to the tooth,wherein the engagement portions of at least some of the second pluralityof appliance shells are each arranged to contact the convex surface atthe same location so as to apply similar repositioning forces to thetooth.

In another aspect, a computer-implemented method for processing toothmovement data in order to design an orthodontic system for repositioninga patient's teeth is provided. The computer system receives toothmovement data indicative of a movement trajectory for a tooth of thepatient, and processes data including the tooth movement data so as todetermine a geometry for an attachment device to be coupled to thetooth, the attachment device comprising a convex surface. The computersystem further processes data including the tooth movement data so as todetermine geometries for a plurality of appliance shells, each shaped toreceive the patient's teeth. The plurality of appliance shells for whichthe geometries are determined each comprise an engagement portionpositioned to engage the convex surface of the attachment device so asto apply a repositioning force to the tooth. Optionally, the engagementportions of at least some of the plurality of appliance shells may eachbe arranged to contact the convex surface at a different respectivelocation so as to apply different respective repositioning forces to thetooth in order to move the tooth along the movement trajectory.

In many embodiments, the attachment device comprises a single convexsurface.

In many embodiments, the convex surface comprises a spherical,ellipsoidal, or cylindrical surface profile.

In many embodiments, each engagement portion of each appliance shellcomprises a planar surface, and the repositioning force applied by eachengagement portion is oriented along a direction substantially normal tothe planar surface. In some embodiments, the planar surfaces of the atleast some of the plurality of appliance shells are each arranged at adifferent orientation relative to the convex surface.

In many embodiments, the different respective repositioning forcesdiffer from each other with respect to one or more of location ororientation.

In many embodiments, the method further comprises calculating one ormore forces or moments to move the tooth along the movement trajectory.The different repositioning forces applied correspond to at least asubset of the one or more forces or moments.

In many embodiments, the movement trajectory comprises a non-linearmovement trajectory.

In many embodiments, the movement trajectory is configured to produceround-tripping of the tooth. As used herein, “round-tripping” may referto a sequence of movements in which a tooth moves away from an initialposition and/or orientation (e.g., to avoid colliding with anothertooth) and then moves at least partially back towards the initialposition and/or orientation.

In many embodiments, each engagement portion is positioned so as tocontact the convex surface of the attachment device at a singlelocation.

In many embodiments, at least one of the plurality of appliance shellscomprises a plurality of engagement portions positioned to contact theconvex surface at a plurality of different locations.

In many embodiments, the attachment device further comprises anon-contacting surface that does not engage the plurality of applianceshells. The non-contacting surface may be a convex surface or anon-convex surface.

In many embodiments, the method further comprises outputting digitaldata indicative of the determined geometries of the plurality ofappliance shells.

In another aspect, an orthodontic appliance for repositioning apatient's teeth is provided. The appliance comprises an attachmentdevice configured to be coupled to a tooth of the patient and comprisinga convex surface, as well as a shell comprising a plurality of cavitiesshaped to receive the patient's teeth. At least one cavity of theplurality of cavities comprises a receptacle shaped to receive theattachment device, and the receptacle comprises a planar surfacepositioned to engage the convex surface of the attachment device so asto apply a repositioning force to the tooth. Optionally, the planarsurface is positioned to engage the convex surface at a single locationto apply the repositioning force to the tooth.

In many embodiments, the convex surface comprises a spherical,ellipsoidal, or cylindrical shape profile.

In many embodiments, the repositioning force applied by the planarsurface is oriented along a direction substantially normal to the planarsurface.

In many embodiments, the attachment device further comprises anon-contacting surface that does not engage the planar surface. Thenon-contacting surface may be a convex surface or a non-convex surface.

In another aspect, an orthodontic system for repositioning a patient'steeth is provided. The system comprises an attachment device configuredto be coupled to a tooth of the patient and comprising a convex surface.The system also comprises a plurality of appliance shells each shaped toreceive the patient's teeth, each appliance shell comprising anengagement portion positioned to engage the convex surface of theattachment device so as to apply a repositioning force to the tooth. Inmany embodiments, the engagement portions of at least some of theplurality of appliance shells are each arranged to contact the convexsurface at the same location so as to apply repositioning forces to thetooth.

In many embodiments, the attachment device comprises a single convexsurface.

In many embodiments, the convex surface comprises a spherical,ellipsoidal, or cylindrical shape profile.

In many embodiments, each engagement portion of each appliance shellcomprises a planar surface, and the repositioning force applied by eachengagement portion is oriented along a direction substantially normal tothe planar surface. The amount of friction between the planar surface ofthe engagement portion and the convex surface of the attachment devicemay be relatively low resulting in minimal or no tangential forces. Insome embodiments, the planar surfaces of the at least some of theplurality of appliance shells are arranged at the same orientationrelative to the convex surface.

In many embodiments, each engagement portion is positioned so as tocontact the convex surface of the attachment device at a singlelocation.

In many embodiments, the attachment device further comprises anon-contacting surface that does not engage the plurality of applianceshells. The non-contacting surface may be a convex surface or anon-convex surface.

In many embodiments, the system further comprises a second plurality ofappliance shells each shaped to receive the patient's teeth, eachappliance shell of the second plurality of appliance shells comprisingan engagement portion positioned to engage the convex surface of theattachment device so as to apply a repositioning force to the tooth,wherein the engagement portions of at least some of the second pluralityof appliance shells are each arranged to contact the convex surface at adifferent location so as to apply different repositioning forces to thetooth.

In another aspect, a computer-implemented method for processing toothmovement data in order to design an orthodontic system for repositioninga patient's teeth is provided. The computer system receives toothmovement data indicative of a movement trajectory for a tooth of thepatient, and processes data including the tooth movement data so as todetermine a geometry for an attachment device to be coupled to thetooth, the attachment device comprising a convex surface. The computersystem further processes data including the tooth movement data so as todetermine geometries for a plurality of appliance shells, each shaped toreceive the patient's teeth. The plurality of appliance shells for whichthe geometries are determined each comprise an engagement portionpositioned to engage the convex surface of the attachment device so asto apply a repositioning force to the tooth. Optionally, the engagementportions of at least some of the plurality of appliance shells may eachbe arranged to contact the convex surface at the same location so as toapply repositioning forces to the tooth in order to move the tooth alongthe movement trajectory.

In many embodiments, the attachment device comprises a single convexsurface.

In many embodiments, the convex surface comprises a spherical,ellipsoidal, or cylindrical surface profile.

In many embodiments, each engagement portion of each appliance shellcomprises a planar surface, and the repositioning force applied by eachengagement portion is oriented along a direction substantially normal tothe planar surface. In some embodiments, the planar surfaces of the atleast some of the plurality of appliance shells are each arranged at thesame orientation relative to the convex surface.

In many embodiments, the method further comprises calculating one ormore forces or moments to move the tooth along the movement trajectory.The repositioning forces applied correspond to at least a subset of theone or more forces or moments.

In many embodiments, each engagement portion is positioned so as tocontact the convex surface of the attachment device at a singlelocation.

In many embodiments, the attachment device further comprises anon-contacting surface that does not engage the plurality of applianceshells. The non-contacting surface may be a convex surface or anon-convex surface.

In many embodiments, the method further comprises outputting digitaldata indicative of the determined geometries of the plurality ofappliance shells.

The embodiments disclosed herein are well suited for combination withone or known commercially available tooth moving components such asattachments and polymeric shell appliances. In many embodiments, theappliance and one or more attachments are configured to move one or moreteeth along a tooth movement vector comprising six degrees of freedom,in which three degrees of freedom are rotational and three degrees offreedom are translation.

The present disclosure provides orthodontic systems and related methodsfor designing and providing improved or more effective tooth movingsystems for eliciting a desired tooth movement and/or repositioningteeth into a desired arrangement.

Although reference is made to an appliance comprising a polymeric shellappliance, the embodiments disclosed herein are well suited for use withmany appliances that receive teeth, for example appliances without oneor more of polymers or shells. The appliance can be fabricated with oneor more of many materials such as metal, glass, reinforced fibers,carbon fiber, composites, reinforced composites, aluminum, biologicalmaterials, and combinations thereof for example. The appliance can beshaped in many ways, such as with thermoforming or direct fabrication(e.g., 3D printing, additive manufacturing), for example. Alternativelyor in combination, the appliance can be fabricated with machining suchas an appliance fabricated from a block of material with computernumeric control machining.

Orthodontic systems of the present disclosure can include toothattachments and one or more orthodontic appliances that engage theattachments when worn by a patient. Appliances having teeth receivingcavities that receive and reposition teeth, e.g., via application offorce due to appliance resiliency, are generally illustrated with regardto FIG. 1A. FIG. 1A illustrates an exemplary tooth repositioningappliance or aligner 100 that can be worn by a patient in order toachieve an incremental repositioning of individual teeth 102 in the jaw.The appliance can include a shell (e.g., a continuous polymeric shell ora segmented shell) having teeth-receiving cavities that receive andresiliently reposition the teeth. An appliance or portion(s) thereof maybe indirectly fabricated using a physical model of teeth. For example,an appliance (e.g., polymeric appliance) can be formed using a physicalmodel of teeth and a sheet of suitable layers of polymeric material. Insome embodiments, a physical appliance is directly fabricated, e.g.,using rapid prototyping fabrication techniques, from a digital model ofan appliance. An appliance can fit over all teeth present in an upper orlower jaw, or less than all of the teeth. The appliance can be designedspecifically to accommodate the teeth of the patient (e.g., thetopography of the tooth-receiving cavities matches the topography of thepatient's teeth), and may be fabricated based on positive or negativemodels of the patient's teeth generated by impression, scanning, and thelike. Alternatively, the appliance can be a generic appliance configuredto receive the teeth, but not necessarily shaped to match the topographyof the patient's teeth. In some cases, only certain teeth received by anappliance will be repositioned by the appliance while other teeth canprovide a base or anchor region for holding the appliance in place as itapplies force against the tooth or teeth targeted for repositioning. Insome cases, some or most, and even all, of the teeth will berepositioned at some point during treatment. Teeth that are moved canalso serve as a base or anchor for holding the appliance as it is wornby the patient. Typically, no wires or other means will be provided forholding an appliance in place over the teeth. In some cases, however, itmay be desirable or necessary to provide individual attachments or otheranchoring elements 104 on teeth 102 with corresponding receptacles orapertures 106 in the appliance 100 so that the appliance can apply aselected force on the tooth. Exemplary appliances, including thoseutilized in the Invisalign® System, are described in numerous patentsand patent applications assigned to Align Technology, Inc. including,for example, in U.S. Pat. Nos. 6,450,807, and 5,975,893, as well as onthe company's website, which is accessible on the World Wide Web (see,e.g., the url “invisalign.com”). Examples of tooth-mounted attachmentssuitable for use with orthodontic appliances are also described inpatents and patent applications assigned to Align Technology, Inc.,including, for example, U.S. Pat. Nos. 6,309,215 and 6,830,450.

FIG. 1B illustrates a tooth repositioning system 110 including aplurality of appliances 112, 114, 116. Any of the appliances describedherein can be designed and/or provided as part of a set of a pluralityof appliances used in a tooth repositioning system. Each appliance maybe configured so a tooth-receiving cavity has a geometry correspondingto an intermediate or final tooth arrangement intended for theappliance. The patient's teeth can be progressively repositioned from aninitial tooth arrangement to a target tooth arrangement by placing aseries of incremental position adjustment appliances over the patient'steeth. For example, the tooth repositioning system 110 can include afirst appliance 112 corresponding to an initial tooth arrangement, oneor more intermediate appliances 114 corresponding to one or moreintermediate arrangements, and a final appliance 116 corresponding to atarget arrangement. A target tooth arrangement can be a planned finaltooth arrangement selected for the patient's teeth at the end of allplanned orthodontic treatment. Alternatively, a target arrangement canbe one of some intermediate arrangements for the patient's teeth duringthe course of orthodontic treatment, which may include various differenttreatment scenarios, including, but not limited to, instances wheresurgery is recommended, where interproximal reduction (IPR) isappropriate, where a progress check is scheduled, where anchor placementis best, where palatal expansion is desirable, where restorativedentistry is involved (e.g., inlays, onlays, crowns, bridges, implants,veneers, and the like), etc. As such, it is understood that a targettooth arrangement can be any planned resulting arrangement for thepatient's teeth that follows one or more incremental repositioningstages. Likewise, an initial tooth arrangement can be any initialarrangement for the patient's teeth that is followed by one or moreincremental repositioning stages.

The various embodiments of the orthodontic appliances presented hereincan be fabricated in a wide variety of ways. As an example, someembodiments of the appliances herein (or portions thereof) can beproduced using indirect fabrication techniques, such as by thermoformingover a positive or negative mold. Indirect fabrication of an orthodonticappliance can involve producing a positive or negative mold of thepatient's dentition in a target arrangement (e.g., by rapid prototyping,milling, etc.) and thermoforming one or more sheets of material over themold in order to generate an appliance shell. Alternatively or incombination, some embodiments of the appliances herein may be directlyfabricated, e.g., using rapid prototyping, stereolithography, 3Dprinting, and the like.

The configuration of the orthodontic appliances herein can be determinedaccording to a treatment plan for a patient, e.g., a treatment planinvolving successive administration of a plurality of appliances forincrementally repositioning teeth. Computer-based treatment planningand/or appliance manufacturing methods can be used in order tofacilitate the design and fabrication of appliances. For instance, oneor more of the appliance components described herein can be digitallydesigned and fabricated with the aid of computer-controlledmanufacturing devices (e.g., computer numerical control (CNC) milling,computer-controlled rapid prototyping such as 3D printing, etc.). Thecomputer-based methods presented herein can improve the accuracy,flexibility, and convenience of appliance fabrication.

In many embodiments, orthodontic appliances, such as the applianceillustrated in FIG. 1A, impart forces to the crown of a tooth and/or anattachment positioned on the tooth at one or more points of contactbetween a tooth receiving cavity of the appliance and received toothand/or attachment. The magnitude of each of these forces and/or theirdistribution on the surface of the tooth can determine the type oforthodontic tooth movement which results. Tooth movements may be in anydirection in any plane of space, and may comprise one or more ofrotation or translation along one or more axes. Types of tooth movementsinclude extrusion, intrusion, rotation, tipping, translation, and rootmovement, and combinations thereof. Tooth movement of the crown greaterthan the movement of the root can be referred to as tipping. Equivalentmovement of the crown and root can be referred to as translation.Movement of the root greater than the crown can be referred to as rootmovement.

FIG. 2 illustrates a method 200 of orthodontic treatment using aplurality of appliances, in accordance with many embodiments. The method200 can be practiced using any of the appliances or appliance setsdescribed herein. In step 210, a first orthodontic appliance is appliedto a patient's teeth in order to reposition the teeth from a first tootharrangement to a second tooth arrangement. In step 220, a secondorthodontic appliance is applied to the patient's teeth in order toreposition the teeth from the second tooth arrangement to a third tootharrangement. The method 200 can be repeated as necessary using anysuitable number and combination of sequential appliances in order toincrementally reposition the patient's teeth from an initial arrangementto a target arrangement. The appliances can be generated all at the samestage or time point, in sets or batches (e.g., at the beginning of oneor more stages of the treatment), or one at a time, and the patient canwear each appliance until the pressure of each appliance on the teethcan no longer be felt or until the maximum amount of expressed toothmovement for that given stage has been achieved. A plurality ofdifferent appliances (e.g., a set) can be designed and even fabricatedprior to the patient wearing any appliance of the plurality. Afterwearing an appliance for an appropriate period of time, the patient canreplace the current appliance with the next appliance in the seriesuntil no more appliances remain. The appliances are generally notaffixed to the teeth and the patient may place and replace theappliances at any time during the procedure (e.g., patient-removableappliances). The final appliance or several appliances in the series mayhave a geometry or geometries selected to overcorrect the tootharrangement. For instance, one or more appliances may have a geometrythat would (if fully achieved) move individual teeth beyond the tootharrangement that has been selected as the “final.” Such over-correctionmay be desirable in order to offset potential relapse after therepositioning method has been terminated (e.g., permit movement ofindividual teeth back toward their pre-corrected positions).Over-correction may also be beneficial to speed the rate of correction(e.g., an appliance with a geometry that is positioned beyond a desiredintermediate or final position may shift the individual teeth toward theposition at a greater rate). In such cases, the use of an appliance canbe terminated before the teeth reach the positions defined by theappliance. Furthermore, over-correction may be deliberately applied inorder to compensate for any inaccuracies or limitations of theappliance.

The orthodontic systems described herein can include one or moretooth-mounted attachment devices (also referred to herein as“attachments”) that engage a portion of an orthodontic appliance, suchas a shell appliance, in order to apply a force to the underlying tooth.An attachment device can be fabricated using various methods. Forexample, a pre-formed attachment device (e.g., directly fabricated byrapid prototyping, 3D-printing, etc.) having a specified geometry can bebonded to the patient's tooth at a target location on the tooth surfaceusing light-curable adhesives and the like. Alternatively, theattachment can be formed in situ on the patient's tooth using a templatehaving a recess defining the attachment geometry, the recess beingfilled with a curable material. In many embodiments, the template is ashell appliance that, when worn on the patient's teeth, positions therecess filled with material over the target location on the toothsurface. The material can then be cured, e.g., with light energy, inorder to form and bond the attachment to the tooth surface.

Use of attachment devices may be advantageous for exerting repositioningforces that would otherwise be difficult to achieve using a shellappliance alone. In many embodiments, an attachment device includes oneor more surfaces arranged to engage (e.g., contact) a correspondingportion of an appliance shell when the shell is worn on patient's teeth,and the engagement between the attachment surface(s) and shell portioncan produce forces that elicit tooth movement. The geometry (e.g., size,shape) and/or location (e.g., position, orientation) of the attachmentdevice can be varied as desired to produce the desired tooth movementforce(s). For example, the attachment devices herein can be any suitableshape, such as a portion of a sphere, ellipse, ovoid, cylinder, or acurved and/or flat polyhedral shape. In many embodiments, the portion ofthe appliance that touches the tooth may be shaped to substantiallymatch the shape of the tooth surface. Similarly, as described above andherein, the surface(s) of an attachment device that engage the appliancecan have any suitable shape, such as a spherical, ellipsoidal, orcylindrical shape profile, or even further profiles that comprise asubstantially convex curve along at least one dimension. In someembodiments, at least one surface of an attachment device that engagesthe appliance may be substantially planar.

In many embodiments, the appliance shell is shaped to accommodate theattachment device when the shell is placed on the patient's teeth. Forexample, the appliance shell can include an engagement portionpositioned to engage (e.g., contact) one or more surfaces of theattachment device. Optionally, the engagement portion can be part of areceptacle or recess in the appliance shell that receives the attachmentor a portion thereof. The engagement portion can have any suitableshape, such as substantially planar, convex, or even concave surfaces.The engagement portion can have a shape complementary to that of theattachment surface(s) in order to provide mating contact with thesurface(s) when the appliance is worn, e.g., a planar engagement portionis used in combination with a planar attachment surface. The engagementportion can alternately have a shape that differs substantially from theshape of the attachment surface, such as an engagement portioncomprising a substantially planar surface in combination with a convexattachment surface, or a convex appliance surface in combination with asubstantially planar attachment surface. In many embodiments, theengagement portion of the appliance includes a surface having acurvature that differs from the curvature of the correspondingattachment surface(s).

The various surfaces of attachments and appliances are described hereinvariously using terms such as “planar,” “convex,” or “concave.” It willbe further understood that when using each of these terms, included inthe idea are surfaces substantially similar to such surfaces. Thus,planar surfaces as described herein include substantially planarsurfaces, convex surfaces include substantially convex surfaces, andconcave surfaces include substantially concave surfaces. In someembodiments, surface irregularities or roughness, such as those due tomanufacturing limitations, may be ignored in defining convex, concave,or planar surfaces if they are small compared to the size of the surfaceas a whole (e.g., at least one or two orders of magnitude smaller).Thus, for example, an approximately ellipsoidal surface portion with asurface area of 4 square mm and a depth of 1 mm from edge to outermostpoint would be considered to be a substantially convex surface, even ifit had surface irregularities, for example, on the 0.1 mm scale.

The curvature of a convex surface, such as a convex surface of anattachment, may be chosen in a variety of ways. For example, the convexsurface may be shaped like a portion of a sphere or an ellipsoid, or maybe a shape substantially similar to such a surface, such as ovoidshapes, for example. Other surfaces may be also chosen, such as portionsof cylindrical surfaces, which may be used to allow variable forcedirections around the radius of the cylinder without allowingsubstantial variation along the axis of the cylinder.

The curvature of an attachment surface or appliance surface can becharacterized in a variety of ways. For example, the degree of concavityor convexity may be determined based on the radius of curvature of thesurface. In some embodiments, a concave or convex surface of anattachment or appliance has a radius of curvature less than or equal toabout 10 mm, less than or equal to about 50 mm, less than or equal toabout 100 mm, less than or equal to about 150 mm, or less than or equalto about 200 mm. In some embodiments, the radius of curvature is withina range from about 0.5 mm to about 10 mm, within a range from about 1 mmto about 10 mm, within a range from about 3 mm to about 10 mm, within arange from about 10 mm to about 50 mm, within a range from about 10 mmto about 100 mm, within a range from about 10 mm to about 200 mm, withina range from about 50 mm to about 100 mm, within a range from about 50mm to about 150 mm, within a range from about 50 mm to about 200 mm,within a range from about 100 mm to about 150 mm, or within a range fromabout 150 mm to about 200 mm. In some embodiments, a planar surface ofan attachment or appliance has as radius of curvature of greater than orequal to about 10 mm.

In some embodiments, the degree of concavity or convexity of anattachment surface may be determined based on the ratio of the radius ofcurvature of the surface to the half-size of the attachment. The term“half-size” may be used herein to refer to the radius of the circlehaving a surface area equivalent to the lateral surface area (e.g.,surface area attached to the tooth surface) of the attachment. In someembodiments, a convex or concave attachment surface has a radius ofcurvature that is approximately the same order of magnitude as thehalf-size of the attachment. In some embodiments, the ratio of radius ofcurvature to half-size for a convex or concave attachment surface isless than or equal to about 50. In some embodiments, the ratio of radiusof curvature to half-size for a planar attachment surface is greaterthan or equal to about 50.

As another example, the ratio of the depth to a size of a surface may beused to characterize it as substantially planar, convex, or concave. Thesize of a surface may be determined by taking the square root of itsarea. The depth of a surface may be determined as follows: given a planethat minimizes the mean square distance from the plane to the perimeterof the surface, the depth is the sum of the distances in each directionfrom that plane to the farthest point on the surface. In someembodiments, the attachments herein include convex surfaces wherein thesize-to-depth ratio is within a range from about 1:100 to about 1:10, orwithin a range from about 1:10 to about 1:2. In further embodiments, anattachment can have a convex surface with a size-to-depth ratio of about1, or within a range from about ½ to about 2, or even larger ratios,such as within a range from about 2 to about 10, within a range fromabout 10 to about 100, or even greater.

FIG. 3 illustrates the interface between an attachment comprising aplanar surface and an engagement portion of an appliance comprising aplanar surface. An attachment 310 comprising a planar surface 320 isbonded to a tooth 300. Part of an orthodontic shell appliance 330 isshown as worn in the mouth of a patient, the appliance having anengagement portion comprising a planar surface 340. Optionally, theappliance 330 can include a recess or receptacle shaped to receive theattachment 310 or a portion thereof, and the planar surface 340 of theengagement portion can form part of the recess or receptacle. Theorthodontic appliance 330 is designed such that when worn, the planarsurface 340 of the engagement portion engages the planar surface 320 ofthe attachment 310. This engagement produces a force 350 on theattachment 310. Because the attachment 310 is bonded to the tooth 300,the force 350 causes a tooth moving force 360, and may also apply amoment 370 on the tooth 300.

The magnitude and direction of the tooth moving force 360 may bedetermined by the shape and/or material properties of the orthodonticappliance 330 and of the attachment 310. The magnitude of the toothmoving force 360 may depend on the elasticity of the appliance 330, theattachment (e.g., the attachment 310 is typically a relatively rigidmaterial compared to the appliance), and the degree to which the planarappliance surface 340 is deflected from its unloaded or rest state whenit comes into contact with the planar attachment surface 320. Thedirection of the tooth moving force may be determined by the angle atwhich the attachment surface 320 and appliance surface 340 come intocontact. In some embodiments, friction may be relatively low forappliance and attachment surfaces contacting within a patient's mouth,so the force 350, as well as corresponding tooth moving force 360, willpoint in a direction substantially normal to the engaged appliance andattachment surfaces, which may be designed to be parallel orsubstantially parallel to each other.

The moment 370 may be determined by the magnitude and direction of thetooth moving force 360 as well as the displacement vector from thecenter of rotation 380 of the tooth to the location of engagementbetween surfaces 320 and 340, e.g., as a vector cross-product of thetooth moving force 360 and the displacement vector. In embodiments whereplanar surfaces such as appliance surface 340 and attachment surface 320are designed to be parallel, the contact location of the surfaces may beapproximated as the center of the two surfaces. However, if the twosurfaces contact each other at an unintended location, for example dueto imperfect fabrication of the appliance and/or attachment, undesiredforces and moments can be produced. For example, if an appliance and anattachment are fabricated with planar surfaces that are notsubstantially parallel, they may only contact at the edge of thesurfaces, rather than continuously across the center of the surfaces asintended. This can result in forces and/or moments that differdramatically from the expected values, which may in turn lead to anunwanted tooth movement.

FIGS. 4A and 4B illustrate how small errors in appliance fabrication canlead to large changes in the location of interaction between a planarappliance surface and a planar attachment surface.

FIG. 4A illustrates an appliance 430 with an engagement portioncomprising an appliance surface 440 configured to engage an attachmentsurface 420 of a dental attachment 410. In the depicted embodiment, theintended appliance surface 441 is oriented parallel to the attachmentsurface 420, in order to produce a desired force 450 at or near thecenter 451 of the attachment surface. However, if the actual appliancesurface 440 is oriented at an angle rotated counterclockwise from theintended surface 441, e.g., due to imperfect manufacturing, theappliance instead produces a force 452 located near the end of theattachment surface 420, at contact location 453. Because the engagementsurfaces are substantially planar, even a very small change in angle ofthe appliance surface 440 can cause a large difference in contactlocation. This can result in a moment vector being applied to the tooththat is significantly different from the desired value.

FIG. 4B shows a similar problem that can occur when the angle of anappliance surface has an error in the opposite direction. An appliance435 with an engagement portion comprising an appliance surface 445 isconfigured to engage an attachment surface 425 of a dental attachment415. The intended appliance surface 446 is parallel to the attachmentsurface 425, in order to produce a desired force 455. This isillustrated by intended surface 446. However, if the actual appliancesurface 445 is oriented at an angle rotated clockwise from the intendedsurface 446, e.g., due to imperfect manufacturing, the appliance insteadproduces a force 457 located near the end of the attachment surface 425,at contact location 458. Because the attachment and appliance surfacesare planar, even a very small change in angle of the appliance surface440 can cause a large difference in contact location. This can result ina moment vector being applied to the tooth that is significantlydifferent from the desired value. Furthermore, because the contactlocation 458 is at an edge of the attachment surface 425, the magnitudeand direction of the resulting force 457 may differ significantly fromthe desired force 455. Furthermore, the sharp attachment corner atcontact location 458 can cause the magnitude of resulting force 457 todepend strongly on the shape of the attachment corner, such that smallmanufacturing imperfections can lead to large changes in force magnitudeand/or direction.

As illustrated by FIGS. 4A and 4B, the use of attachments with planarsurfaces to engage appliances with planar surfaces can lead todifficulties in creating desired forces and moments, with smallmanufacturing defects or variations leading to large changes in forceand/or moment. Such manufacturing defects or variations may arise due toinaccuracies in fabricating the appliance (e.g., by direct fabricationor indirect fabrication via thermoforming over a mold), as well asinaccuracies in fabricating the attachment device, and can result in anappliance and/or attachment geometry that differs from the intendedgeometry (e.g., with respect to shape, position, and/or orientation).Furthermore, even absent manufacturing defects, providing properengagement between attachment and appliance means that planar attachmentsurfaces may be limited in the range of planar appliance surfaces theycan engage: for example, if the two planes are not substantiallyparallel, they may interact in unpredictable or undesirable ways. Whenfriction is relatively low, a configuration of parallel planes can belimited in some instances to only producing a force in a singledirection: substantially normal to the surface of the attachment.

In some embodiments, the attachment devices and appliances disclosedherein address these issues by replacing the engaged planar surface ofan attachment with a convex surface, allowing different appliances to bemanufactured to produce different forces, while also making the systemas a whole more robust against manufacturing defects.

FIG. 5A illustrates an attachment with a convex surface and a portion ofan appliance shell configured to engage that surface, in accordance withembodiments. An attachment 510 with a convex attachment surface 520 isbonded to a tooth 500. The attachment 510 can be used in conjunctionwith an appliance shell 530 with a receptacle to accommodate and receivethe attachment 510. The appliance 530 includes an engagement portioncomprising an appliance surface 540 that contacts the convex attachmentsurface 520 at contact location 551, generating a force 550 on theattachment 510, and thus a similar tooth moving force on the tooth 500to which the attachment is bonded.

In many embodiments, the engagement portion of the appliance comprisesan appliance surface 540 that is substantially planar, as depicted.However, in alternative embodiments, it may also be designed to beconvex (bending away from the attachment), or even concave (bendingtoward the attachment). In embodiments where the engagement surface isconcave, the magnitude of its curvature may be less than that of theconvex attachment surface so as to permit contact with the convexattachment surface at a single location. The curvature of the applianceand the attachment away from the contact location may be varied asdesired. For example, in some embodiments, appliance 530 also comprisesa concave portion 560 with greater curvature than the convex attachmentengagement surface 520, but because the concave portion 560 does notengage the convex attachment engagement surface 520, the force appliedby the contact between the appliance and the attachment is not affected.One of ordinary skill in the art would appreciate that since the innersurface of the appliance contacts the outer surface of the attachment, aconvex attachment engagement surface has the same absolute direction ofcurvature as a concave appliance engagement surface, and vice versa.

In the depicted embodiment, the appliance surface 540 is arranged tocontact the convex attachment surface 520 at a single location 551 onthe attachment 510 such that the force 550 is applied to the tooth 500localized about that location. The position of contact location 551 isdetermined by the shape of the convex attachment surface 520 and theslope of the appliance surface 540: in the case of a planar applianceengagement surface, for example, the two may contact at the point wherethe appliance surface is substantially tangent to the attachmentsurface. The direction of force can likewise be determined by the twosurfaces: when friction is low, the force 550 may be determined to be ina direction substantially normal to the two engagement surfaces at theircontact location 551, with minimal or no force components are producedalong the direction tangential to the attachment surface. “Substantiallynormal” may be used herein to refer to an angle within a range fromabout 89° to about 91°, from about 85° to about 95°, or from about 75°to about 105°. Thus, it can be appreciated that the direction of theapplied tooth moving force can be determined—and varied—by varying thelocation and orientation of the appliance surface relative to theattachment device, thereby changing both the location and orientation ofthe resultant tooth moving force.

FIG. 5B illustrates a plurality of appliances, each configured with asurface at a different angle so as to contact a single attachment atdifferent locations, thereby applying different forces, in accordancewith embodiments. In each of configurations 502, 504, and 506, adifferent respective shell appliance 532, 534, and 536 engages the sameattachment 510. Each appliance has a respective engagement portioncomprising an appliance surface 542, 544, and 546, each surface beingoriented at a different respective angle 543, 545, and 547. Thedifferent angles of the surfaces of appliances 532, 534, and 536 causethe engagement portion of each appliance to engage the convex surface ofattachment 510 at a different respective location 553, 555, and 557,thereby producing different respective tooth moving forces 552, 554, and556, in a direction substantially normal to the respective appliancesurfaces 542, 544, and 546. Due to the different contact locations 553,555, and 557, in conjunction with the different tooth moving forces 552,554, and 556, it will likewise be appreciated that each applianceapplies a different moment to the tooth as well. Thus, a singleattachment comprising a convex surface may be used to produce aplurality of different forces and/or a plurality of different moments,by sequentially contacting a plurality of appliances to the attachmentat different locations. It will be appreciated that in many embodiments,the force direction applied by each appliance shell may be independentlychosen from a substantially continuous distribution by designing theappliance such that the engagement portion contacts the attachmentsurface at a location chosen from a corresponding, substantiallycontinuous distribution of contact locations along the attachmentsurface. This permits the movement of a tooth along a complex,continuously variable trajectory using only a single attachment, asdiscussed further herein.

In many embodiments, an attachment device comprises only a singlecontinuous convex surface. In alternative embodiments, an attachmentdevice may comprise a plurality of different surfaces. These surfacesmay comprise multiple convex surfaces, or even mixes of convex, concave,and/or planar surfaces. In some embodiments, an appliance may beconfigured to concurrently engage a plurality of attachment surfaces,such as a plurality of convex attachment surfaces or even a mixture ofattachment surfaces. For example, an appliance might concurrently and/orsequentially engage both convex and planar surfaces of an attachment. Insome embodiments, the attachment device includes one or morenon-contacting surfaces that do not engage (e.g., contact) any portionof the appliance surface when the appliance is worn by the patient. Thegeometry of a non-contacting surface may be varied as desired, e.g.,planar, convex, or non-convex.

FIG. 6 illustrates a tooth 600 to which is bonded an attachment 610comprising both a convex surface 620 and a non-contacting surface 625.FIG. 6 also illustrates an appliance 630 with an engagement portioncomprising a surface 640 configured to engage the convex surface 620, inaccordance with embodiments. As illustrated in the figure, the convexsurface 620 protrudes outward, presenting a contact location 651 that istangent to the appliance engagement surface 640, and at which the twowill meet. The tooth moving force 650 applied by the appliance points ina direction substantially normal to both the appliance surface 640 andthe convex attachment surface 620 at their point of contact 651. As canbe readily appreciated, the direction of force may be varied smoothly byvarying the angle of appliance surface 640, for example using aplurality of appliances, which will also correspondingly smoothly shiftthe point of contact 651.

The attachment 610 may also include a non-contacting surface 625 thatdoes not engage (e.g., contact) the appliance 630, and therefore doesnot directly transmit force from the appliance 630 to the tooth 600. Thegeometry of the non-contacting surface 625 may be varied as desired(e.g., convex, concave, or planar). Further illustrated by a dotted lineis alternative surface 622, which extends the convex surface 622 so thatthe entire exposed surface of attachment 610 would comprise a singleconvex surface. The attachment size and shape implied by alternativesurface 622 may be too large for comfort or aesthetic reasons. Thus, itmay be desirable in some embodiments to design attachments such asattachment 610 which only comprise convex surfaces where engagement withthe appliance is desired, while eliminating unwanted volume where theappliance is not intended to engage the attachment so as to formnon-contacting surfaces (e.g., surface 625).

In many embodiments, the appliances herein are designed to contact theconvex surface of an attachment device at a single location. Inalternative embodiments, an appliance can be designed to concurrentlycontact a single attachment device at a plurality of differentlocations, e.g., at 2, 3, 4, 5, or more different locations. In manyembodiments, the different locations may be positioned along a singleconvex surface. In many embodiments, some of the different locations maybe located on different sides of an attachment. In many embodiments,some of the different locations may be located on the same side of anattachment. In many embodiments, some of the different locations may belocated on different convex surfaces of the attachment device. In manyembodiments, one engagement portion of an appliance may contact aplurality of different locations on one or more attachment surfaces.

FIG. 7A illustrates an attachment with a convex surface and an appliancewith a plurality of surfaces, each configured to concurrently contactthe convex surface at different respective locations so as to apply aforce to a tooth, in accordance with many embodiments. An attachment 710(e.g., with an approximately ellipsoidal shape) is shown from aperspective facing toward the surface of a tooth 700, corresponding tothe plane of the page. The attachment comprises a convex surface 720configured to engage an appliance at a plurality of locations, whereineach location determines a particular force and a particular moment. Inthe illustrated embodiment, the attachment surface 720 is engaged by anappliance 730 with engagement portions comprising a plurality ofsurfaces 740 and 745. The appliance surfaces concurrently engage theconvex surface 720 at separate respective contact locations 751 and 756,producing respective contact forces 750 and 755. In the depictedembodiment, these two forces add together to produce a net tooth movingforce 760 pointing in an upwards direction. In alternative embodiments,the appliance may engage the attachment devices at other contactlocations so as to produce forces in other directions. Thisconfiguration allows a net tooth moving force to be produced in adirection that is not substantially normal to either contacted surface.Furthermore, the different directions and locations of contact forces750 and 755 may cause each to produce a moment on the tooth. Thecombination of these moments can produce a net moment which can havesome components larger or smaller than those of either of the individualcontacts, optionally at or near zero.

A further benefit of using more than one point of contact betweenappliance surfaces and convex attachment surfaces is to allow anappliance to apply tooth moving forces in directions where directengagement with an attachment would be difficult to achieve oruncomfortable for the patient. FIG. 7B illustrates an alternativeconfiguration of the attachment and appliance of FIG. 7A, in which eachappliance surface contacts a separate convex surface of the attachment,in accordance with many embodiments. An attachment 712 with a pluralityof convex attachment surfaces 722 and 724 is shown from a perspectivefacing toward the surface of a tooth 702, corresponding to the plane ofthe page. Convex surfaces 722 and 724 are configured to engageengagement portions of an appliance at a plurality of locations, whereineach location determines a particular force and a particular moment. Theconvex surfaces 722 and 724 are optionally separated by a non-convexsurface 726, such that attachment 712 does not extend as far down fromits center as attachment 710 of FIG. 7A. This feature can be useful insituations where size or shape of the attachment is constrained, forexample, when an ellipsoidal attachment would extend too far towards thegum line of the patient or make an undercut shape that is difficult fora removable appliance to engage.

Each attachment surface 722 and 724 is respectively engaged byengagement portions of an appliance 732 with a plurality of respectivesurfaces 742 and 747. The appliance surfaces concurrently engage therespective convex surfaces 722 and 724 at separate respective contactlocations 753 and 758, producing respective contact forces 752 and 757.In the depicted embodiment, these two forces add together to produce anet tooth moving force 762 pointing in an upwards direction. Thisconfiguration of appliance and attachment allows an upwards force, suchas an extrusion force, to be applied to a tooth, for example, whilekeeping both the attachment and the appliance from extending too fartowards the patient's gum line. In alternative embodiments, theappliance may engage the attachment devices at other contact locationsso as to produce forces in other directions.

FIG. 7C illustrates an attachment with a convex surface and an appliancewith a plurality of surfaces, each configured to concurrently contactthe convex surface at different respective locations so as to apply anet moment to a tooth, in accordance with many embodiments. Anattachment 714 (e.g., with an approximately ellipsoidal shape) is shownfrom a perspective facing toward the surface of a tooth 704,corresponding to the plane of the page. The attachment comprises aconvex surface 724 configured to engage an appliance at a plurality oflocations, wherein each location determines a particular force and aparticular moment. In the illustrated embodiment, the attachment surface724 is engaged by an appliance 734 with engagement portions comprising aplurality of surfaces 744 and 749. The appliance surfaces concurrentlyengage the convex surface 724 at separate respective contact locations761 and 763, producing respective contact forces 754 and 759. These twoforces may be about equal in magnitude and approximately opposite indirection, so they produce a net force of about zero. However, due totheir different contact locations 761 and 763, they produce respectivemoments that add together to produce a moment 770 in a clockwisedirection about center of rotation 780. This configuration allows amoment to be produced by contacting a single attachment with surfaces ofa single appliance without needing to apply a tooth moving force.Although the attachment is illustrated here as approximately ellipsoidalwith a single convex surface similar to that of FIG. 7A, other shapesmay readily be used, including shapes with separate convex surfaces suchas illustrated in FIG. 7B. It will be further appreciated that theelements illustrated in FIGS. 7A-C may be freely combined; for example,to allow both a net force and a net moment to be independentlydetermined by concurrently contacting the convex surfaces of anattachment with engagement surfaces of an appliance at one, two, or evenmore locations. Additionally, other forces may also be applied to theattachment or tooth in combination with those depicted in FIGS. 7A-C,e.g., to inhibit undesirable tooth movements, as would be understood byone of ordinary skill in the art.

It will be understood by one of skill in the art that in someembodiments the roles played by the attachment and the appliance may bereversed; for example, the attachment may comprise a planar surfaceengaged by an appliance engagement portion comprising a convex appliancesurface. This reversed design allows the application of a plurality ofparallel tooth-moving forces, each substantially normal to the planarattachment surface, and each arising from a different contact point.This allows a variable moment to be applied to a tooth while applyingtooth moving forces that may be similar in direction and/or magnitude.Further embodiments may employ attachments that have a mix of engagementsurface types—for example, some convex surfaces and some planarsurfaces—in order to further customize the forces and moments that maybe applied to the patient's tooth. In each case, one or more appliancesmay be fabricated to properly engage the respective attachment surfaces;for example, in some cases convex attachment surfaces may be engaged byplanar appliance surfaces while planar attachment surfaces are engagedby convex appliance surfaces. In some cases, different attachmentsurface types may be engaged concurrently, in a manner similar to thatdepicted in FIGS. 7A and 7B, in order to provide differential momentsand/or combined forces.

FIGS. 8A-8D illustrate the reduced sensitivity of attachments engaged onconvex surfaces to manufacturing variations, compared to attachmentsengaged on planar surfaces. As described further herein, this reducedsensitivity allows a more accurate and reliable application of toothmoving force. This can allow more precise tooth movements to beperformed, as well as decrease the rate at which unintended toothmovements are produced.

FIG. 8A illustrates the reduced sensitivity of attachments with convexsurfaces to defects in appliance fabrication. An orthodontic system 800is shown, comprising an attachment 810 with a convex surface 820 bondedto a tooth in order to allow the application of a tooth moving forcewhen engaged by an engagement portion of an appliance 830. Orthodonticappliance 830 is illustrated with an engagement portion comprising aplanar surface 840. Further illustrated is an alternate surface 841,which comprises a plane at a slightly different angle than surface 840.Due to manufacturing inaccuracies, an appliance intended to befabricated with surface 840 might instead be fabricated with surface841.

When surface 840 is brought into contact with attachment surface 820, itapplies a force 850 at a contact location 851. By contrast, when surface841 is brought into contact with attachment surface 820, it applies adifferent force 860 at a contact location 861. The difference in anglesof the forces is approximately equal to the difference in angle of theplanar surfaces 840 and 841. Similarly, the difference in force locationis small, as can be seen by the small distance between contact locations851 and 861. Thus, the difference in moment applied to tooth can be keptsmall, since the moment depends on the force and the contact location,neither of which has greatly changed.

In contrast to FIG. 8A, FIG. 8B illustrates the increased sensitivity ofattachments with planar surfaces to defects in appliance fabrication. Anorthodontic system 802 is shown, comprising an attachment 812 with aplanar surface 822 bonded to a tooth in order to allow the applicationof a tooth moving force when engaged by an engagement portion anappliance 832. Orthodontic appliance 832 is illustrated with anengagement portion comprising a planar surface 842. Further illustratedis an alternate surface 843, which comprises a plane at a slightlydifferent angle than surface 842. Due to manufacturing inaccuracies, anappliance intended to be fabricated with surface 842 might instead befabricated with surface 843.

When surface 842 is brought into contact with attachment surface 822, itapplies a force 852 at a contact location 853. By contrast, when surface843 is brought into contact with attachment surface 822, it applies adifferent force 862 at a contact location 863. The difference in anglesof the forces is not large, similar to the difference illustrated inFIG. 8A. However, the difference in force location is large, as can beseen by the large distance between contact locations 853 and 863. Thedifference in moment applied to tooth will be much larger than incorresponding FIG. 8A, since the moment depends on the force and thecontact location, and the contact location has changed by a much largeramount: as illustrated, the distance between the two contact locationsis nearly the full length of the planar surface 822. Thus, it can beappreciated that attachments with convex surfaces may be much lesssusceptible to appliance manufacturing errors than attachments withplanar surfaces.

FIG. 8C illustrates the reduced sensitivity of attachments with convexsurfaces to defects in attachment fabrication. An orthodontic system 804is shown, comprising an attachment 814 with a convex surface 824 bondedto a tooth in order to allow the application of a tooth moving forcewhen engaged by an engagement portion of an appliance 834. Orthodonticappliance 834 is illustrated with an engagement portion comprising aplanar surface 844. Further illustrated is an alternate convex surface825 of attachment 814, in which the left end of the convex surface 825protrudes less than in convex surface 824. Due to manufacturinginaccuracies, an attachment intended to be fabricated with convexsurface 824 might instead be fabricated with convex surface 825. Thelatter configuration of appliance and attachment is illustrated withdashed lines.

When appliance surface 844 is brought into contact with convexattachment surface 824, it applies a force 854 at a contact location855. By contrast, when appliance surface 844 is brought into contactwith attachment surface 825, it applies a different force 864 at acontact location 865. The appliance surface also translates to adifferent position in order to maintain contact. As can be seen in FIG.8C, the contact location shifts a moderate amount between locations 855and 865, due to the significant difference in shape of the convexsurfaces 824 and 825, and the resulting movement of the appliancesurface 844. However, despite this shift, the direction of forces 854and 864 are substantially the same. This is because, in each case, theappliance surface is angled in the same direction, so that the force itapplies—being substantially normal to the appliance surface so long asfriction is low—points in substantially the same direction as well.Thus, an attachment with a convex surface can apply forces that are lesssensitive to manufacturing defects of the convex surfaces.

In contrast to FIG. 8C, FIG. 8D illustrates the increased sensitivity ofattachments with planar surfaces to defects in attachment fabrication.An orthodontic system 806 is shown, comprising an attachment 816 with aplanar surface 826 bonded to a tooth in order to allow the applicationof a tooth moving force when engaged by an engagement portion of anappliance 836. Orthodontic appliance 836 is illustrated with anengagement portion comprising a planar surface 846. Further illustratedis an alternate planar surface 827 of attachment 816, in which theplanar surface 827 is fabricated at a different angle than that ofplanar surface 826. Due to manufacturing inaccuracies, an attachmentintended to be fabricated with planar surface 826 might instead befabricated with planar surface 827. The latter configuration ofappliance and attachment is illustrated with dashed lines.

When appliance surface 846 is brought into contact with planarattachment surface 826, it applies a force 856 at a contact location857. By contrast, when appliance surface 846 is brought into contactwith attachment surface 827, it applies a different force 866 at acontact location 867. The appliance surface also translates to adifferent position in order to maintain contact. As can be seen in FIG.8D, the contact location shifts dramatically between locations 857 and867, due to the difference in angle of planar surfaces 826 and 827, andthe resulting movement of the appliance surface 846. Furthermore, thedirection of forces 856 and 866 change as well. This can be seen fromthe fact that, although the appliance surface is angled in the samedirection, the contact location shifts substantially, so that contactlocation 857 is beyond the end of planar surface 846, while contactlocation 867 is beyond the end of planar surface 827. Thus, in eachcase, the force applied may depend on the shape of the edges of theengagement portions of the appliance, rather than on the central, planarsurface of the engagement portions as intended. This leads to anunpredictable force that varies strongly even with small imperfectionsin manufacturing. It can further be appreciated that, since both theforce and the contact location change more in FIG. 8D than incorresponding FIG. 8C, the potential for variation in moment due tomanufacturing defects is also greater for planar attachment surfacesthan for convex surfaces.

The convex attachment devices described herein can be used incombination with a plurality of orthodontic appliances in order toproduce complex tooth movement trajectories that involve sequentialapplication of forces along different directions and/or at differentlocations. For example, the tooth movement trajectories may benon-linear trajectories, such as curved trajectories or trajectorieswith a variable tooth movement velocity (e.g., accelerating ordecelerating movements). Some trajectories may comprise “round-tripping”motion, in which a tooth is moved in one direction away from an initialposition and/or orientation, then later in an opposing direction atleast partially towards to the initial position and/or orientation.Round-tripping may be beneficial, for example, to move an obstructingtooth away from the path of another tooth. In some cases, a tooth may bemoved in a substantially straight line despite applying forces atdifferent angles, because the applied forces act to oppose other forcesincident on the tooth. In some cases, a portion of a trajectory mayinvolve no motion of a tooth; for example, to allow other teeth to movein the meantime. Two or more sequential trajectories, whether complex orsimple, may be combined to form an overall trajectory, which may becomplex. Such combination may be repeated as desired to make anarbitrarily complex trajectory.

FIGS. 9A-9E illustrate how a tooth may be moved in a complex trajectorywhile applying forces to a single attachment comprising one or moreconvex surfaces, in accordance with embodiments.

FIG. 9A illustrates a tooth 900 bonded to an attachment 910 with aconvex surface. In the depicted embodiment, the tooth 900 is desired tomove to a target location 990, but cannot travel in a straight linebecause an obstructing tooth 905 is partially in the way. For thisreason, a curved trajectory 980 is planned to move tooth 900 from itsstarting position to its target location 990. The first step isaccomplished by fabricating an appliance with an engagement portioncomprising a surface that engages the attachment's convex surface at acontact location 951 on the left side of the attachment, applying aforce 950 pushing the tooth in a distal direction, toward the right ofthe image.

FIG. 9B shows the tooth 900 as it first begins moving. A first appliancecontacts the attachment 910 at a contact location 953 chosen to producea tooth moving force 952 that continues to push the tooth distally.

FIG. 9C illustrates the tooth 900 farther along its trajectory. Now thatthe tooth 900 is mostly clear of the obstructing tooth 905, the angle offorce 954 is shifted by fabricating a second appliance to contact tocontact the attachment 910 at a point 955 so as to apply a force pointedmore toward the lingual direction at the top of the page.

FIG. 9D illustrates the tooth 900 after fully clearing the obstructingtooth 905. The tooth 900 no longer needs to move distally, so a thirdappliance is fabricated with an engagement portion with a surface tocontact the convex surface of attachment 910 at a point 957, therebyapplying a force 956 in a lingual direction.

FIG. 9E shows the tooth 900 after arriving at its target location, inthe desired alignment with tooth 905. At this point, orthodontictreatment may stop and attachment 910 may be removed. Alternately, iffurther movement of tooth 900 is desired (for example, extrusion,intrusion, translation, or rotation), then additional appliances may befabricated with engagement portions comprising one or more surfacesconfigured to contact attachment 910 at the appropriate points to applythe required tooth moving forces.

FIGS. 10A-10E illustrate the use of an attachment comprising one or moreconvex surfaces to rotate a tooth in multiple directions to providespace to move a second tooth, thereby allowing a complex reorganizationof teeth, in accordance with embodiments.

FIG. 10A illustrates a configuration of teeth in which a first tooth1005 is desired to move to a target location 1090. In the depictedembodiment, a second tooth 1000 obstructs the straight line path. Inorder to rearrange the teeth to the desired configuration, the firsttooth 1005 may be moved along a curved trajectory 1080, while the secondtooth 1000 may be sequentially rotated: first with a clockwise rotation1082, then with a counterclockwise rotation 1084 to return it to itsoriginal orientation.

FIG. 10B illustrates the starting position, in which a rotationalmovement is caused to the second tooth 1000 by applying a force 1050 toan attachment 1010 with a convex surface by engaging that surface with afirst appliance at a contact location 1051. This produces a moment 1070on the tooth 1000, causing a rotation of the tooth in a clockwisedirection. Optionally, other forces (not shown) may also be applied toinhibit any translational movements elicited by the force 1050.

FIG. 10C illustrates a new tooth configuration in which the second tooth1000 has been rotated to a position where it no longer obstructs thefirst tooth 1005. The first tooth 1005 is then moved along a trajectory1080 to its target location. This movement may be accomplished usingattachments with convex surfaces, as described in detail in FIGS. 9A-E,or by other methods; for example, using one or more conventionalattachments, using appliances acting directly on tooth 1000, etc.

FIG. 10D illustrates the configuration of teeth 1000 and 1005 after thefirst tooth 1005 has arrived at its target location. The second tooth1000 is now to be rotated to its original orientation, which requires acounterclockwise rotation. Accordingly, a second appliance is fabricatedwith an engagement portion with a surface configured to contactattachment 1010 at location 1053, thereby applying a force 1052 in therightwards direction. This force produces a moment 1072 that causes arotation of tooth 1000 in a counterclockwise direction. Optionally,other forces (not shown) may also be applied to inhibit anytranslational movements elicited by the force 1052.

FIG. 10E illustrates the final configuration of teeth 1000 and 1005 witheach tooth in its desired location and orientation. At this point,orthodontic treatment may stop and attachment 1010 may be removed.Alternately, if further movement of tooth 1000 or tooth 1005 is desired(for example, extrusion, intrusion, translation, or rotation), thenappliances may be fabricated with one or more engagement portionscomprising one or more surfaces configured to contact attachment 1010(or a corresponding attachment on tooth 1005) at the appropriate pointsto apply the required tooth moving forces.

FIG. 11 illustrates a method 1100 of treating a patient using anattachment comprising a convex surface and one or more appliances, inaccordance with embodiments. The method 1100, as with all other methodsherein, can be used in combination with any embodiment of the attachmentdevices and appliances provided herein.

In step 1110, an attachment device comprising a convex surface iscoupled to a patient's tooth. The attachment device may be mounted onthe tooth by bonding the device to a surface of a tooth, using adhesive,for example. Alternatively, attachment may be molded and cured in situ,e.g., using a template appliance having an appropriately shaped recessto define the shape of the attachment. The position, orientation, andsurface geometry of the attachment device may be chosen so as to allowthe application of desired tooth moving forces by one or moreappliances.

In step 1120, an appliance is supplied to the patient for placement inthe patient's mouth. The shell of the appliance comprises an engagementportion arranged to contact the convex surface at a first location,thereby applying a tooth moving force at that location, and in adirection that is substantially normal to the surface of the attachmentat the first location. This tooth moving force may cause a movement ofthe tooth along a desired trajectory. In some cases, the desiredtrajectory may be that the tooth be prevented from moving, in which casethe tooth moving force may be applied to counteract an otherwiseexpected movement. Additionally or alternatively, the tooth moving forcemay be applied to reduce, prevent, or reverse a movement in a particulardirection, while allowing or causing movement in another direction.

In step 1130, a second appliance is supplied to the patient forplacement in the patient's mouth. The shell of the appliance comprisesan engagement portion arranged to contact the convex surface at a firstlocation, thereby applying a tooth moving force at that location, and ina direction that is substantially normal to the surface of theattachment at the first location. This tooth moving force may cause amovement of the tooth along a desired trajectory. In some cases, thedesired trajectory may be that the tooth be prevented from moving, inwhich case the tooth moving force may be applied to counteract anotherwise expected movement. Additionally or alternatively, the toothmoving force may be applied to reduce, prevent, or reverse a movement ina particular direction, while allowing or causing movement in anotherdirection.

Step 1130 is optional, and may be omitted. For example, step 1130 may beunnecessary if step 1120 was sufficient to arrange the patient's teethas desired. Step 1130 may also be unnecessary if orthodontic correctionafter step 1120 is to be performed without orthodontic appliances orwithout use of the convex-surfaced attachment. Alternatively, step 1130may be repeated as many times as needed, applying to the patient's tootha third appliance, fourth appliance, fifth appliance, and so on toaccomplish long and/or complex movements of teeth.

FIG. 12 illustrates a method 1200 of designing appliances andattachments to treat a patient, in accordance with embodiments. Method1200 may be performed by a data processing system, as disclosed herein.

In step 1210, tooth movement data are received indicative of a movementtrajectory for a tooth of a patient. The tooth movement data maycomprise a starting position and target position of one or more teeth,as well as trajectories over which the one or more teeth are desired tobe moved. The positions of further teeth not desired to be moved mayalso be specified. The indicated movement trajectories may comprise anordered sequence of movements, and different teeth may be movedconcurrently or sequentially as part of the overall movement trajectoryof the teeth. In some embodiments, the movement paths are configured tomove the teeth in the quickest fashion with the least amount ofround-tripping to bring the teeth from their initial positions to theirdesired target positions. Alternatively, some round tripping may beused; for example, to allow other aspects of the movement paths to beeasier to perform. The tooth paths can optionally be segmented, and thesegments can be calculated so that each tooth's motion within a segmentstays within threshold limits of linear and rotational translation. Inthis way, the end points of each path segment can constitute aclinically viable repositioning, and the aggregate of segment end pointscan constitute a clinically viable sequence of tooth positions, so thatmoving from one point to the next in the sequence does not result in acollision of teeth.

In step 1220, the system processes data including the tooth movementdata so as to determine a geometry for an attachment device comprising aconvex surface to be coupled to the tooth. To determine the geometry ofthe attachment device, a force system to produce movement of the one ormore teeth along the movement path may be determined. A force system caninclude one or more forces and/or one or more moments. Different forcesystems can result in different types of tooth movement, such astipping, translation, rotation, extrusion, intrusion, root movement,etc. Biomechanical principles, modeling techniques, forcecalculation/measurement techniques, and the like, including knowledgeand approaches commonly used in orthodontia, may be used to determinethe appropriate force system to be applied to the tooth to accomplishthe tooth movement. In determining the force system to be applied,sources may be considered including literature, force systems determinedby experimentation or virtual modeling, computer-based modeling,clinical experience, minimization of unwanted forces, etc.

Based on the set of forces and/or moments identified to cause the toothmovement, an attachment geometry may be determined. The attachmentgeometry may include an attachment surface shape as well as anattachment position and orientation of the surface of a tooth. In somecases, a plurality of attachments may be chosen for attachment to one ormore teeth. The attachment surface shape may be chosen to allow forcesto be applied by one or more appliance surfaces contacting theattachment at one or more respective locations. For example, anattachment may be designed with one or more convex surfaces, wherein foreach force and/or moment to be applied to the attachment, that forceand/or moment may be applied by contacting an appliance surface to theattachment at one or more locations on one or more of its convexsurfaces. In some cases, the choice of attachment surface shape may bemade by choosing from a set of pre-designed surfaces, such as spherical,ellipsoidal, or cylindrical surface portions. In further cases, theattachment surface shape may be custom designed based on the set offorces and/or moments desired; for example, a convex surface may bedesigned by identifying a solid angle large enough to include alldesired forces, then choosing a convex surface large enough to includeat least the identified solid angle.

In step 1230, the system processes data including the tooth movementdata so as to determine geometries for one or more appliance shellsshaped to fit the patient's teeth. The appliance shells may compriseengagement portions with surfaces configured to engage one or moreconvex surfaces of the attachments identified in step 1220 at locationschosen to apply the desired forces and/or moments needed to cause thetooth movements along the trajectory identified in step 1210. In somecases, an appliance may comprise a plurality of surfaces to engage oneor more convex surfaces of an attachment, so as to produce combined ordifferential forces and/or moments. In cases involving a plurality ofappliance shells, each shell may have independently configuredengagement portions with respective independently configured surfaces,allowing each shell to apply an independently chosen force and/or momentby engaging one or more convex attachment surfaces at independentlydetermined locations. By applying these appliances sequentially to thepatient's teeth, a sequence of tooth movements may be caused, the neteffect of which is to move one or more teeth along controlledtrajectories over time. Each appliance may be designed to properlyreceive the patient's teeth in the positions they are expected to be inat the time the appliance is to be worn, and these designs may beupdated over time, for example, if further measurements of the patient'steeth indicate that one or more teeth are not moving as predicted.

FIG. 13 illustrates a method for digitally planning an orthodontictreatment, in accordance with embodiments. The method 1300 can beapplied to any of the treatment procedures described herein and can beperformed by any suitable data processing system. Any embodiment of theappliances or attachments described herein can be designed or fabricatedusing the method 1300.

In step 1310, a digital representation of a patient's teeth is received.The digital representation can include surface topography data for thepatient's intraoral cavity (including teeth, gingival tissues, etc.).The surface topography data can be generated by directly scanning theintraoral cavity, a physical model (positive or negative) of theintraoral cavity, or an impression of the intraoral cavity, using asuitable scanning device (e.g., a handheld scanner, desktop scanner,etc.).

In step 1320, one or more treatment stages are generated based on thedigital representation of the teeth. The treatment stages can beincremental repositioning stages of an orthodontic treatment proceduredesigned to move one or more of the patient's teeth from an initialtooth arrangement to a target arrangement. For example, the treatmentstages can be generated by determining the initial tooth arrangementindicated by the digital representation, determining a target tootharrangement, and determining movement paths of one or more teeth in theinitial arrangement necessary to achieve the target tooth arrangement.The movement path can be optimized based on minimizing the totaldistance moved, preventing collisions between teeth, avoiding toothmovements that are more difficult to achieve, or any other suitablecriteria.

In step 1330, at least one orthodontic appliance is fabricated based onthe generated treatment stages. For example, a set of appliances can befabricated to be sequentially worn by the patient to incrementallyreposition the teeth from the initial arrangement to the targetarrangement. Some of the appliances can be shaped to accommodate a tootharrangement specified by one of the treatment stages. Alternatively orin combination, some of the appliances can be shaped to accommodate atooth arrangement that is different from the target arrangement for thecorresponding treatment stage. For example, as previously describedherein, an appliance may have a geometry comprising an engagementportion with a surface to engage a particular location of a convexsurface of an attachment bonded to a patient's tooth, so as to apply adesired force and/or moment to the tooth. Such an appliance may be usedto ensure that a suitable amount of force is expressed on the teeth asthey approach or attain their desired target positions for the treatmentstage. As another example, an appliance can be designed in order toapply a specified force system on the teeth and may not have a geometrycorresponding to any current or planned arrangement of the patient'steeth.

In some instances, staging of various arrangements or treatment stagesmay not be necessary for design and/or fabrication of an appliance. Asillustrated by the dashed line in FIG. 13, design and/or fabrication ofan orthodontic appliance, and perhaps a particular orthodontictreatment, may include use of a representation of the patient's teeth(e.g., receive a digital representation of the patient's teeth 1310),followed by design and/or fabrication of an orthodontic appliance basedon a representation of the patient's teeth in the arrangementrepresented by the received representation.

FIG. 14 is a simplified block diagram of a data processing system 1400that may be used in executing methods and processes described herein.The data processing system 1400 typically includes at least oneprocessor 1402 that communicates with one or more peripheral devices viabus subsystem 1404. These peripheral devices typically include a storagesubsystem 1406 (memory subsystem 1408 and file storage subsystem 1414),a set of user interface input and output devices 1418, and an interfaceto outside networks 1416. This interface is shown schematically as“Network Interface” block 1416, and is coupled to correspondinginterface devices in other data processing systems via communicationnetwork interface 1424. Data processing system 1400 can include, forexample, one or more computers, such as a personal computer,workstation, mainframe, laptop, and the like.

The user interface input devices 1418 are not limited to any particulardevice, and can typically include, for example, a keyboard, pointingdevice, mouse, scanner, interactive displays, touchpad, joysticks, etc.Similarly, various user interface output devices can be employed in asystem of the invention, and can include, for example, one or more of aprinter, display (e.g., visual, non-visual) system/subsystem,controller, projection device, audio output, and the like.

Storage subsystem 1406 maintains the basic required programming,including computer readable media having instructions (e.g., operatinginstructions, etc.), and data constructs. The program modules discussedherein are typically stored in storage subsystem 1406. Storage subsystem1406 typically includes memory subsystem 1408 and file storage subsystem1414. Memory subsystem 1408 typically includes a number of memories(e.g., RAM 1410, ROM 1412, etc.) including computer readable memory forstorage of fixed instructions, instructions and data during programexecution, basic input/output system, etc. File storage subsystem 1414provides persistent (non-volatile) storage for program and data files,and can include one or more removable or fixed drives or media, harddisk, floppy disk, CD-ROM, DVD, optical drives, and the like. One ormore of the storage systems, drives, etc may be located at a remotelocation, such coupled via a server on a network or via theinternet/World Wide Web. In this context, the term “bus subsystem” isused generically so as to include any mechanism for letting the variouscomponents and subsystems communicate with each other as intended andcan include a variety of suitable components/systems that would be knownor recognized as suitable for use therein. It will be recognized thatvarious components of the system can be, but need not necessarily be atthe same physical location, but could be connected via variouslocal-area or wide-area network media, transmission systems, etc.

Scanner 1420 includes any means for obtaining a digital representation(e.g., images, surface topography data, etc.) of a patient's teeth(e.g., by scanning physical models of the teeth such as casts 1421, byscanning impressions taken of the teeth, or by directly scanning theintraoral cavity), which can be obtained either from the patient or fromtreating professional, such as an orthodontist, and includes means ofproviding the digital representation to data processing system 1400 forfurther processing. Scanner 1420 may be located at a location remotewith respect to other components of the system and can communicate imagedata and/or information to data processing system 1400, for example, viaa network interface 1424. Fabrication system 1422 fabricates appliances1423 based on a treatment plan, including data set information receivedfrom data processing system 1400. Fabrication machine 1422 can, forexample, be located at a remote location and receive data setinformation from data processing system 1400 via network interface 1424.

While preferred embodiments of the present disclosure have been shownand described herein, it will be obvious to those skilled in the artthat such embodiments are provided by way of example only. Numerousvariations, changes, and substitutions will now occur to those skilledin the art without departing from the invention. It should be understoodthat various alternatives to the embodiments of the invention describedherein may be employed in practicing the invention. Numerous differentcombinations of embodiments described herein are possible, and suchcombinations are considered part of the present disclosure. In addition,all features discussed in connection with any one embodiment herein canbe readily adapted for use in other embodiments herein. It is intendedthat the following claims define the scope of the invention and thatmethods and structures within the scope of these claims and theirequivalents be covered thereby.

What is claimed is:
 1. A computer-implemented method for digitallyplanning treatment of a patient's teeth, the method comprising:identifying a treatment plan for a patient's dentition to move one ormore teeth of the patient's dentition from a starting position toward adesired target position along a movement path; determining one or moreforces to move the one or more teeth in the patient's dentition inaccordance with at least a portion of the movement path; determining oneor more geometries of one or more convex attachment devices that, incombination with corresponding engagement portions of one or more innersurfaces of a plurality of dental appliances, implement at least aportion of the one or more forces, the one or more convex attachmentdevices comprising one or more convex surfaces to engage thecorresponding engagement portions of the one or more inner surfaces ofthe plurality of dental appliances, wherein a shape of the one or moreconvex attachment devices is characterized by a portion of a cylinderhaving a radius of curvature; and providing instructions to display avirtual representation of the one or more convex attachment devices on avirtual model of the patient's dentition.
 2. The method of claim 1,wherein at least one of the one or more convex attachment devicescomprises a single convex surface.
 3. The method of claim 2, wherein thesingle convex surface comprises a spherical, ellipsoidal, or cylindricalsurface profile.
 4. The method of claim 1, wherein each of thecorresponding engagement portions comprises a planar surface, and therepositioning force applied by each of the corresponding engagementportions is oriented along a direction substantially normal to theplanar surface.
 5. The method of claim 4, wherein the planar surfaces ofthe at least some of the plurality of dental appliances are eacharranged at a different orientation relative to the corresponding convexsurface.
 6. The method of claim 1, further comprising calculating one ormore forces or moments to move the one or more teeth along the movementpath.
 7. The method of claim 1, wherein the movement path comprises anon-linear movement trajectory.
 8. The method of claim 1, wherein themovement path is configured to produce round-tripping of the tooth. 9.The method of claim 1, wherein each of the corresponding engagementportions is positioned so as to contact the one or more convex surfacesat a single location.
 10. The method of claim 1, wherein at least one ofthe plurality of dental appliances comprises a plurality of engagementportions positioned to contact the one or more convex surfaces at aplurality of different locations.
 11. The method of claim 1, wherein theone or more convex attachment devices further comprise a non-contactingsurface that does not engage the plurality of dental appliances.
 12. Themethod of claim 1, further comprising displaying the virtualrepresentation of the one or more convex attachment devices on thevirtual model of the patient's dentition.
 13. The method of claim 1,further comprising providing instructions to fabricate the one or moreconvex attachment devices.
 14. The method of claim 1, further comprisingproviding instructions to fabricate the one or dental appliances. 15.The method of claim 1, further comprising providing modifying thetreatment plan to implement the one or more convex attachment devices.16. The method of claim 1, wherein determining the one or moregeometries of the one or more convex attachment devices comprisesdetermining a surface profile used to form the one or more convexsurfaces.
 17. The method of claim 1, wherein: determining the one ormore geometries of the one or more convex attachment devices comprisesdetermining a surface profile used to form the one or more convexsurfaces; and the surface profile comprises a shape based on a set ofpre-defined surfaces.
 18. The method of claim 1, wherein: determiningthe one or more geometries of the one or more convex attachment devicescomprises determining a surface profile used to form the one or moreconvex surfaces; and the surface profile comprises a spherical surfaceprofile, an ellipsoidal surface profile, a cylindrical surface profile,or some combination thereof.
 19. The method of claim 1, wherein:determining the one or more geometries of the one or more convexattachment devices comprises determining a surface profile used to formthe one or more convex surfaces; and the surface profile is based on ashape with a custom design.
 20. The method of claim 1, whereindetermining the one or more geometries of the one or more convexattachment devices comprises determining the one or more shapes of theone or more convex surfaces.
 21. The method of claim 1, whereindetermining the one or more geometries of the one or more convexattachment devices comprises determining the one or more positions ofthe one or more attachment devices, one or more orientations of the oneor more attachment devices, or some combination thereof.